查询词典 kernel of integral operator

Algorithm application of neural networks.Ⅲ Implementation of neuro-computers. The main contribution of the dissertation can be summarized as follows: 1 Hopf bifurcation of three kind of neural networks are discussed in detail, including type of discrete time delay, type of time delay with weak kernel and strong kernel as well as the proof of existence of bifurcation. Other problems such as asymptotic stability of bifurcation periodic solution, algorithm of determining the bifurcation direction, asymptotic stability and style of periodic solution are also studied. The average time delay is chosen as the bifurcation parameter, phenomena pertinent to system states of the continuous time delay network with strong kernel evolving from stable to oscillating, then back to stable again are observed.

论文的主要创新之处可以归纳如下： 1）针对目前国内外对神经网络的分岔研究较少的情况，论文中详细讨论了带离散时延神经网络、带弱核的连续时延神经网络、带连续分布时延且具有强核的神经网络的Hopf分岔现象，从理论上证明了Hopf分岔的存在性，并研究了分岔周期解的渐近稳定性，得到了确定周期解的渐近稳定性、分岔方向、周期解的渐近形式的算法；用平均时延作为分岔参数，发现带强核的连续时延神经网络中存在着系统的状态由稳定变化到振荡现象，当继续增加平均时延参数时，又从振荡变为稳定这一特殊的动力学现象。

Dorea advanced kernel estimation p of p ,which is a general density with respect to a σ-finite measure v on.ξ is a σ-field of subsets of ER. Some qualities have been gotten. And it has been proved that those results consist of theories of classical kernel estimation for continual density and further extended theories of disperse kernel estimation.

Y Dorea在2001年提出了关于上的σ-有限测度v的一般密度函数P的核估计几，其中ER，ξ是E的一个σ-域，得到了一些结果，并且验证了所得结论包含经典的连续密度核估计的结论，还进一步延伸了离散分布核估计的结论。

Inspired by the intuitive geometric interpretation of SVM based on convex hulls, KNNCH maps the data in the original space to the kernel space with the kernel trick and constructs a nearest neighbor classifier in the kernel space, which takes the convex hulls of training sets as the extended class sets.

该算法的设计受到支持向量机几何解释启发，利用核函数方法将数据映射到高维核空间，并在核空间构造以训练集凸包为扩展类集的最近邻分类器。

Numerical results show that constant coagulation kernel has more influences on small particles than linear and quadratic coagulation kernel,whereas has less influences on big particles than linear and quadratic coagulation kernel;in the same wa...

发现常凝并核要比线性和二次方凝并核对小颗粒的影响大一些、对大颗粒的影响小一些，线性和二次方凝并核对颗粒尺度分布的时间演变影响则取决于具体情况；常冷凝核要比线性冷凝核对小颗粒的影响大一些、对大颗粒的影响小一些；连续区布朗凝并核类似于常凝并核；扩散冷凝核对颗粒尺度分布的影响界于常冷凝核和线性冷凝核之间。

Topics covered include: density estimation (incorporating such topics as kernel density estimates, nearest neighbor estimates, variable kernel methods, orthogonal series estimates, maximum penalized likelihood estimates, bandwidth choice), nonparametric regression (incorporating kernel methods, spline methods, penalized likelihood, bandwidth choice, generalized additive models), and bootstrapping.

非参数建模专题：非参数建模专题：基于计算机的非参数统计方法论。包括：密度估计(如：核密度估计，最近邻估计，可变核方法，正交序列估计，最大补偿似然估计法，带宽选择)非参数回归(如：，核方法，样条方法，补偿似然估计，带宽选择，广义可加模型，)和 bootstrapping 方法。

Firstly, a two-dimension tensor product space is constructed, in which reproducing kernel exists. Secondly a multiresolution analysis is constructed in the reproducing kernel space. Then an orthonormal basis in is obtained. Thus,the reproducing kernel space can be expressed by wavelets spaces. Wavelets approximation formula and sampling formula can also be obtained in the space. Besides, the wavelets approximation formula is simple and easy for calculation. That completes the theory of multiresolution analysis in finite interval fully and provides theoretical base and algorithm for application.

首先，构造二维张量积空间，并证明该空间具有再生核；其次在再生核空间中，建立多尺度分析，获得该空间的一个标准正交基，使得再生核空间可以由小波空间来刻画，进而得到小波级数和相应的采样公式，而且给出的小波级数形式简单易于数值分析，进一步完善了有限区间上的多尺度分析方法，也为实际应用提供了良好的理论基础和算法。

The method improves performance of KPCA by reasonably combining a local conditionally positive definite kernel and a global kernel. The experiment results indicate the new kernel function certainly improves the performance of KPCA.

利用组合核函数提高核主分量分析的性能，该方法将一个全局核函数与一个新的局部核函数条件正定核函数进行合理组合，从而提高KPCA所提取特征的质量。

Through analyses, we can make the conclusion that, the relation of seed fresh weight dry weight and days after pollination, fat percent content, protein nut content, starch nut content can be expressed with Logistic equation; the change of kernel volume, moisture content of kernel and days after pollination accorded with three ascend curve equation. Kernel protein content, starch content and the changes of days after pollination tallied with reciprocal equation and they had high relation.

经过统计与分析，可以看出籽粒鲜重积累量与授粉后时间、籽粒干重与授粉后的时间、脂肪净含量、脂肪百分含量、蛋白质净含量、淀粉净含量与授粉后的时间均可以用Logistic方程描述，籽粒体积变化与授粉后的时间关系表现为三次上升型曲线方程；籽粒的水分含量与授粉后的时间关系表现为三次下降型曲线方程；籽粒中蛋白质百分含量与授粉后时间的动态变化规律、籽粒中淀粉百分含量与授粉后时间的动态变化规律符合倒数方程，均具有较高的拟合度。

By using testing functions to make comparative research on the precision of approximate models which were built by RBF under the condition of different sample amounts and different kernel function types, a conclusion was drawn: the model quality built by Reciprocal Multiquadric RBF as kernel function was highest when the sample amout was big, and the model quality built by Gaussian RBF as kernel function was highest when the sample amount was small.

运用测试函数对在不同样本数量与不同核函数形式下所建立的近似模型的精度进行对比研究，得出逆多二次函数与高斯函数作为核函数分别在大样本和小样本情况下精度最高的结论，并验证了径向基函数近似模型方法能够兼顾效率与精度。

Then, we focus on the construction of a new type of kernels. It has been pointed out that the kernel function of SVM is equivalent to the reproducing kernel of a certain Reproducing Kernel Hilbert Space.

首先对线性核函数、Gaussian核函数等已经用于广泛实践的核函数的性能给出了简要评述，然后重点构造了一类新的核函数。

Objective:To compare the response control and attention of Schizophrenic patients with that of the healthy controls by Integrated Visual and Auditorycontinuous performance test. To quantitate the impairment of cognitive function in patients, and to explore the relationship between cognitive function and the severity of the disorder.

目的：探讨精神分裂症病人在IVA持续操作测试中的反应控制能力、注意力等，并与健康人进行比较，从而量化精神分裂症病人的认知功能损害，并进一步探讨其认知功能与疾病严重程度的关系。

Main effective factors including subcooling degree, mechanical vibration, gas hydrate reformation, environment temperature, noncondensing gas and surfactant are analyzed.

指出过冷度、机械振动、重复生成水合物、环境温度、不凝性气体、添加剂是影响气体水合物生成的主要因素，还对R152a水合物的放冷进行了实验研究。